Dynamic load-absorbing materials and articles

ABSTRACT

A compound for protection of an object from a blast or shock wave. The compound include a matrix material and at least a first and second sets of inclusions in the matrix material that differ in size, quantity, shape and/or composition in a direction through the impact-absorbing material, the combination of which contributes to the ability of the material to exhibit at least one property that changes as the inclusions are deformed in response to a blast or shock wave.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part application of InternationalPatent Application No. PCT/US2012/54335, filed on Sep. 8, 2012, entitledDYNAMIC LOAD-ABSORBING MATERIALS AND ARTICLES which claims the benefitof Provisional Patent Application No. 61/532,676, filed Sep. 9, 2011,entitled IMPACT ABSORBING MATERIALS AND ARTICLES FORMED THEREWITH, eachapplication is hereby incorporated by reference in its entirety into thepresent application.

FIELD OF THE INVENTION

Some embodiments of the present invention pertain to materials thatabsorb and dissipate energy from impacts, and in particular embodimentspertaining to resilient materials the collapse of which occursprogressively among a plurality of feature lengths, or material forwhich the vibratory response occurs progressively among a plurality offeature lengths.

BACKGROUND OF THE INVENTION

Materials capable of absorbing impacts find a wide variety of uses,including protective gear and equipment such as helmets for sportingactivities, motorcycles and bicycles. While significant advances havebeen achieved in impact-absorbing materials, the majority of fatalmotorcycle and bicycle-related deaths involve head injuries, of which atleast some could be prevented by improved helmet designs. Americanfootball is another example of an activity in which head injuries occur,reportedly at a rate of more than 36,000 head injuries per year.

What is needed are impact-absorbing materials that provide improveddissipation of energy. Various embodiments of the present invention dothis in novel and nonobvious ways.

SUMMARY OF THE INVENTION

A compound for protection of an object from a blast or shock wave isdisclosed. The compound includes a matrix material including at leastthree sizes of stress-concentrating features, including a plurality offirst features having a first average characteristic dimension ofbetween about ten microns and about two hundred microns, a plurality ofsecond features having a second average characteristic dimension that isat least about one order of magnitude larger than the first averagecharacteristic dimension, and a plurality of third features having athird average characteristic dimension that is at least about one orderof magnitude larger than the second average characteristic dimension.The material proximate to the first, second, and third featuresprogressively buckles upon application of the load, such that materialproximate the third features tends to deform before the deformation ofmaterial proximate to the second and first features, and materialproximate the first features tends to deform after the deformation ofmaterial proximate to the second and third features. A plurality offeatures belonging to any one of first, second, or third features arefilled with a fluid other than air.

A method of making a blast or shock wave mitigating material isdisclosed. The method includes providing a compound that is curable toform a polymer, providing a mold cavity having an internal heightadapted and configured to produce the polymer suitable to be used in ahelmet or as a sheet of material to be used in blast protection panel,the mold cavity configured to provide geometric features within thecured polymer. The method further includes placing the compound in themold cavity, curing the compound for at least about five minutes,exposing the mixture in the mold cavity to pressure less than ambientpressure after said permitting. The method further includes removing thesubstantially polymerized material from the mold, filling the geometricfeatures with a fluid, and forming the material as an interior portionof a helmet or as the blast protection panel.

BRIEF DESCRIPTION OF THE DRAWINGS

Some of the figures shown herein may include dimensions. Further, someof the figures shown herein may have been created from scaled drawingsor from photographs that are scalable. It is understood that suchdimensions, or the relative scaling within a figure, are by way ofexample, and not to be construed as limiting.

FIG. 1 schematically represents the geometry of a conventional foammaterial and buckling columns defined thereby.

FIG. 2 is a graph representing a typical force-deflection plot of aconventional foam material of the type represented in FIG. 1.

FIG. 3 is a graph representing a force-deflection plot of a type ofimpact-absorbing material according to one embodiment of the presentinvention, and including two embodiments schematically represented inFIG. 3.

FIG. 4 is a graph representing load-displacement plots for threeembodiments of impact-absorbing materials (A, B and C) schematicallyrepresented in FIG. 4.

FIG. 5 is a graph representing strain-deflection plots for theembodiments of the impact-absorbing materials of FIG. 4.

FIGS. 6 and 7 schematically represent perspective views of two types ofreinforcement elements suitable for incorporation into impact-absorbingmaterials in accordance with additional embodiments of the invention.

FIGS. 8 through 14 schematically represent different embodiments ofimpact-absorbing materials in which reinforcement elements of the typesrepresented in FIGS. 6 and 7 have been incorporated in accordance withfurther embodiments of the invention.

FIGS. 15, 16A-B and 17A-D schematically represent different embodimentsof impact-absorbing materials in which reinforcement fiber materialshave been incorporated into the impact-absorbing material of FIG. 8.

FIGS. 18 through 23 represent various but nonlimiting applications forthe impact-absorbing materials of this invention, including theembodiments of FIGS. 3-5 and 8-17.

FIG. 24 is a block diagram representing a process for fabricating animpact-absorbing material according to yet another embodiment of thepresent invention.

FIG. 25 is a photographic representation of a material fabricated fromthe process of FIG. 24.

FIG. 26 is a graphical depiction of stress-strain relationships, showingthe characteristics of material according to yet another embodiment ofthe present invention as compared to several known helmet cushioningmaterials.

FIG. 27. Comparison of the performance of 60Si₄₀40G_(#1) versus paddingmaterials I, II, and III. 60Si₄₀40G_(#) outperforms all materials atimpacts above a 100 g stress level. Material I fails at a 20 g impactlevel, at which point any small increase in strain results in a largeincrease in stress. Materials II and III fail at impacts approximatelyabove a 100 g stress level.

FIG. 28. Comparison of the performance of 60Si80₄₀G_(#1) versus paddingmaterials I, II, and III. 60Si₄₀40G_(#) outperforms all materials atimpacts above a 100 g stress level. Material I fails at a 20 g impactlevel, at which point any small increase in strain results in a largeincrease in stress. Materials II and III fail at impacts approximatelyabove a 100 g stress level. 60Si80₄₀G_(#1) shows minimal signs ofimpending stiffening near 60% compression.

FIG. 4.1. Single degree-of-freedom spring-mass-damper system with rigidmass (m), linear spring constant (K), dashpot (C), input (F(t)), andimpending motion (x).

FIG. 4.3. Schematic of single degree-of-freedom mass-spring-damperexperimental setup with an arbitrary material sample.

FIG. 4.4. Single degree-of-freedom experimental setup, including thestabilized mass spring-damper system, piezoelectric gun, (A) backaccelerometer, and (B) front accelerometer.

FIG. 4.5. Representative energy spectral density for Si₄₀ (a) and Si₈₀(b) pure silicone samples compared to Material I, Material II, andMaterial III materials given an impulse input. Si₄₀ and Material IIIattenuate higher frequencies better than Material I and Material II.

FIG. 4.6. Representative system response to an impulse for pure siliconesamples, Si₄₀ (a) and Si₈₀ (b), compared to Material I, Material II, andMaterial III. Both Si₄₀ and Si₈₀ have responses similar to that of theMaterial III material.

FIG. 4.7. Natural frequency for pure silicone samples is negativelycorrelated to thinning percentage of silicone.

FIG. 4.8. Damping coefficient for pure silicone samples is positivelycorrelated to thinning percentage of silicone.

FIG. 4.9. Representative energy spectral density for Microfyne seriessamples, 70Si₄₀-30G_(MF) (a), 60Si₄₀40G_(MF)(b), 70Si₈₀30G_(MF) (c), and60Si₈₀40G_(MF) (d) compared to Material I, Material II, and Material IIImaterials given an impulse input. The Microfyne series samples haveresponses similar Material I and Material II, with low attenuation athigher frequencies.

FIG. 4.10. Representative system response to an impulse for Microfyneseries samples, 70Si₄₀30G_(MF) (a), 60Si₄₀40G_(MF)(b), 70Si₈₀30G_(MF)(c), and 60Si₈₀40G_(MF)(d), compared to Material I, Material II, andMaterial III. The Si₄₀ samples tend to have responses similar to theMaterial I and Material II, whereas, the Si₈₀ samples tend to haveresponses similar to the Material III.

FIG. 4.11. Both Si₄₀ and Si₈₀ samples have a positive correlationbetween natural frequency and volume fraction of impregnated graphite.The Si₄₀ samples are slightly more sensitive to changes in graphitecontent than the Si₈₀ samples.

FIG. 4.12. Both Si₄₀ and Si₈₀ samples have a positive correlationbetween damping coefficient and volume fraction of impregnated graphite.The Si₄₀ samples are slightly more sensitive to changes in graphitecontent than the Si₈₀ samples

FIG. 4.13. Representative energy spectral density for #2 Medium Flakeseries samples, 70Si₄₀30G_(#2) (a), 60Si₄₀40G_(#2) (b), 70Si₈₀30G_(#2)(c), and 60Si₈₀40G_(#2) (d) compared to Material I, Material II, andMaterial III materials given an impulse input. The Si₄₀ samples haveresponses similar Material I and Material II, with low attenuation athigher frequencies. Attenuation at high frequencies is slightly betterin the Si₈₀ samples.

FIG. 4.14. Representative system response to an impulse for #2 MediumFlake series samples, 70Si₄₀30G_(#2) (a), 60Si₄₀40G_(#2) (b),70Si₈₀30G_(#2) (c), and 60Si₈₀40G_(#2) (d), compared to Material I,Material II, and Material III. Both Si₄₀ and Si₈₀ samples have similarresponses, with notable mitigation of peak amplitude, comparable to theMaterial III response.

FIG. 4.15. Natural frequency of Si₄₀ samples is negatively correlated tovolume fraction of impregnated graphite. Whereas, natural frequency ofSi₈₀ samples is positively correlated to volume fraction of impregnatedgraphite. Si₈₀ samples are more sensitive to changes in graphite contentthan Si₄₀ samples.

FIG. 4.16. The damping coefficient of Si₄₀ samples is negativelycorrelated to volume fraction of impregnated graphite. Whereas, thedamping coefficient of Si₈₀ samples is positively correlated to volumefraction of impregnated graphite. Si₈₀ samples are more sensitive tochanges in graphite content than Si₄₀ samples.

FIG. 4.17. Representative energy spectral density for #1 Large Flakeseries samples, 70Si₄₀30G_(#1) (a), 60Si₄₀40G_(#1) (b), 70Si₈₀30G_(#1)(c), and 60Si₈₀40G_(#1) (d) compared to Material I, Material II, andMaterial III materials given an impulse input. The Si₄₀ samples haveresponses similar Material I and Material II, with low attenuation athigher frequencies. Attenuation at high frequencies is slightly betterin the Si₈₀ samples.

FIG. 4.18. Representative system response to an impulse for #1 LargeFlake series samples, 70Si₄₀30G_(#1) (a), 60Si₄₀40G_(#1) (b),70Si₈₀30G_(#1) (c), and 60Si₈₀40G_(#1) (d), compared to Material I,Material II, and Material III. The Si40 samples tend to have responsessimilar to the Material I and Material II, whereas, the Si₈₀ samplestend to have responses similar to the Material III. The Si₈₀ havedistinctly lower peak magnitudes than the Si₄₀ series.

FIG. 4.19. Both Si₄₀ and Si₈₀ samples have a positive correlationbetween natural frequency and volume fraction of impregnated graphite.The Si₈₀ samples are slightly more sensitive to changes in graphitecontent than the Si₄₀ samples.

FIG. 4.20. Both Si₄₀ and Si₈₀ samples have a positive correlationbetween damping coefficient and volume fraction of impregnated graphite.The Si₈₀ samples are slightly more sensitive to changes in graphitecontent than the Si₄₀ samples.

FIG. 4.21. Representative energy spectral density for All seriessamples, 70Si₄₀30G_(all) (a), 60Si₄₀40G_(All) (b), 70Si₈₀30G_(All) (c),and 60Si₈₀40G_(All) (d) compared to Material I, Material II, andMaterial III materials given an impulse input. The Si₄₀ samples haveresponses similar Material I and Material II, with low attenuation athigher frequencies. Attenuation at high frequencies is slightly betterin the Si₈₀ samples.

FIG. 4.22. Representative system response to an impulse for All seriessamples, 70Si₄₀-30G_(All) (a), 60Si₄₀40G_(All) (b), 70Si₈₀30G_(All) (c),and 60Si₈₀40G_(All) (d), compared to Material I, Material II, andMaterial III. The Si₄₀ samples tend to have responses similar to theMaterial I and Material II, whereas, the Si₈₀ samples tend to haveresponses similar to the Material III, characterized by low peakmagnitude.

FIG. 4.23. Both Si₄₀ and Si₈₀ samples have a positive correlationbetween natural frequency and volume fraction of impregnated graphite.The Si₈₀ samples are slightly more sensitive to changes in graphitecontent than the Si₄₀ samples.

FIG. 4.24. Both Si₄₀ and Si₈₀ samples have a positive correlationbetween damping coefficient and volume fraction of impregnated graphite.The Si₈₀ samples are slightly more sensitive to changes in graphitecontent than the Si₄₀ samples.

FIG. 5.1. Variation of geometry size (a-c), number (d-g), and shape(h-j).

FIG. 5.2. If two materials of the same geometry but different materialproperties are given a uniform strain input, the material with thehigher modulus (Green) will always have the largest area under the curveand therefore, the highest strain energy.

FIG. 5.3. If two materials of the same geometry but different materialproperties are given a uniform stress input, the material with the lowermodulus (Blue) will always have the largest area under the curve andtherefore, the highest strain energy.

FIG. 5.4 is a graphical depiction of the relationship between maximumstrain energy and increasing inclusion diameter according to anotherembodiment of the present invention.

FIG. 5.5 is a graphical depiction of the relationship between maximumstrain energy and volume fraction of cylindrical inclusion according toanother embodiment of the present invention.

FIG. 5.6 is a graphical depiction of the relationship between maximumstrain energy and volume fraction of cylindrical inclusion according toanother embodiment of the present invention.

FIG. 29 is a schematic view of a test cell used for blast testing ablast or shock wave mitigating material.

FIG. 30 is a plot of pressure vs. time for various configurations of theblast or shock wave mitigating material and a reference.

FIG. 31 is a block diagram representing a process for fabricating ablast or shock wave mitigating material according to one embodiment ofthe present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

For the purposes of promoting an understanding of the principles of theinvention, reference will now be made to the embodiments illustrated inthe drawings and specific language will be used to describe the same. Itwill nevertheless be understood that no limitation of the scope of theinvention is thereby intended, such alterations and furthermodifications in the illustrated device, and such further applicationsof the principles of the invention as illustrated therein beingcontemplated as would normally occur to one skilled in the art to whichthe invention relates. At least one embodiment of the present inventionwill be described and shown, and this application may show and/ordescribe other embodiments of the present invention. It is understoodthat any reference to “the invention” is a reference to an embodiment ofa family of inventions, with no single embodiment including anapparatus, process, or composition that should be included in allembodiments, unless otherwise stated. Further, although there may bediscussion with regards to “advantages” provided by some embodiments ofthe present invention, it is understood that yet other embodiments maynot include those same advantages, or may include yet differentadvantages. Any advantages described herein are not to be construed aslimiting to any of the claims.

The use of an N-series prefix for an element number (NXX.XX) refers toan element that is the same as the non-prefixed element (XX.XX), exceptas shown and described thereafter The usage of words indicatingpreference, such as “preferably,” refers to features and aspects thatare present in at least one embodiment, but which are optional for someembodiments. As an example, an element 1020.1 would be the same aselement 20.1, except for those different features of element 1020.1shown and described. Further, common elements and common features ofrelated elements are drawn in the same manner in different figures,and/or use the same symbology in different figures. As such, it is notnecessary to describe the features of 1020.1 and 20.1 that are the same,since these common features are apparent to a person of ordinary skillin the related field of technology.

Although various specific quantities (spatial dimensions, temperatures,pressures, times, force, resistance, current, voltage, concentrations,wavelengths, frequencies, heat transfer coefficients, dimensionlessparameters, etc.) may be stated herein, such specific quantities arepresented as examples only, and further, unless otherwise noted, areapproximate values, and should be considered as if the word “about”prefaced each quantity. Further, with discussion pertaining to aspecific composition of matter, that description is by example only, anddoes not limit the applicability of other species of that composition,nor does it limit the applicability of other compositions unrelated tothe cited composition.

What will be shown and described herein, along with various embodimentsof the present invention, is discussion of one or more tests that wereperformed. It is understood that such examples are by way of examplesonly, and are not to be construed as being limitations on any embodimentof the present invention. It is understood that embodiments of thepresent invention are not necessarily limited to or described by themathematical analysis presented herein.

The invention is directed to impact-absorbing materials orvibration-isolating materials that are capable of absorbingsubstantially more energy than conventional foam materials typicallyused as cushioning materials in various applications, including but notlimited to football, motorcycle, and other types of helmets, as well asother applications in which impacts, shocks, or vibratory inputs are tobe absorbed to protect a living body or inanimate object, the latter ofwhich includes electronic and mechanical systems. Impact-absorbingmaterials of this invention can be tailored to absorb energy, forexample, isolate a person's head from impact (or other multiple-exposureevent), and/or to disrupt blast/shock waves and provide an impedancemismatch so as to ameliorate the effects of blast waves (or other eventsthat tend to occur as a single exposure). Although reference will bemade to impact-absorbing materials, it is understood that such referenceis a non-limiting example, and the various methods and apparatusdescribed herein are also applicable for structures in which transientor stead-state vibratory or acoustic loads (transmitted by any means,including by structure or as gas pressure waves) are encountered andpreferably dissipated.

As will be discussed below, impact-absorbing materials of this inventiongenerally have a functionally graded characteristic as a result ofcontaining hierarchy of inclusions, wherein the inclusions differ insize, quantity, shape and/or composition within the impact-absorbingmaterial to enable the impact-absorbing to absorb substantially moreenergy as a result of the inclusions synergistically cooperating tocause a gradual change in one or more properties of the material. As anonlimiting example, in one embodiment the impact-absorbing materialcomprises a layered or laminate-type structure that includes at leasttwo layers or tier regions, each differing in terms of compositionand/or physical construction. Each of the tier regions comprises amatrix material in which inclusions are dispersed, with at least theinclusions differing in terms of size, quantity, shape and/orcomposition so that the inclusions are hierarchically arranged withinthe impact-absorbing material and, as the impact-absorbing material iscompressed, at least one property of the material gradually andcontinuously changes to absorb more energy than conventional foammaterials. The property may be, for example, the stiffness, elasticity,viscoelasticity, plasticity, and/or failure mode of the material. Thisdistinction is illustrated in FIGS. 2 and 3. FIG. 1 schematicallyrepresents a conventional foam material 10 comprising a solid matrix 12in which pores (voids) 14 are dispersed. The detailed view of FIG. 1represents that the mechanical properties of conventional foam materialsheavily rely on the mechanics of the cell walls 16, which serve asbuckling columns that bear the load of a force applied to the foammaterial 10. The critical buckling force, P_(cr), is determined by theproperties of the cell walls 16, including Young's modulus (E), momentof inertia (I), and length (L), as seen in Equation 1 below.P _(cr)=π² EI/L ²

There are several ways to classify foam materials and analyze commonrelationships, including stress-strain, force-deflection, cyclicbehavior, and stress relaxation. Force-deflection plots are a simple wayto determine the load-bearing characteristics of foam materials. FIG. 2represents a force-deflection plot that demonstrates a flaw of manyflexible foam materials—saturation. Saturation occurs when the loadcontinues to increase, but deflection does not follow the input load,causing large stress concentrations on the contact surface (the surfaceof the material 10 facing the buckling force, P_(cr), in FIG. 1). FIG. 2is a typical force-deflection curve for a conventional foam material ofthe type represented in FIG. 1. FIG. 2 illustrates that, because oftheir load-bearing behavior, foam materials of the type represented inFIG. 1 exhibit a force-deflection curve that is level over a significantportion of the deformation/deflection range. Within the level region ofthe curve, the foam material 10 is not absorbing the load in a mannerthat would safely protect a living body or inanimate object protected bythe material 10.

FIG. 3 represents two embodiments of impact-absorbing materials 20within the scope of the invention, as well as a force-deflection curverepresenting the load-bearing behaviors of the materials 20. Generallyspeaking, each material 20 comprises a solid matrix 22 in whichinclusions 24 are dispersed. The inclusions 24 may be pores (voids) orsome form of solids that fill what would otherwise be voids in thematrix 22. Notably, and as mentioned above, each impact-absorbingmaterial 20 has a layered structure. In the embodiments of FIG. 3, thelayered structure comprises three layers or tier regions 26, 28 and 30,though the use of two tier regions or more than three tier regions isalso within the scope of the invention. The tier regions 26, 28 and 30may be individually formed as discrete layers that are fused, cast,bonded or laminated to each other, or may be integrally formed so thatthe matrix 22 is continuous through the regions 26, 28 and 30.

The tier regions 26, 28 and 30 are represented as differing from eachother in terms of their composition, geometry and/or physicalconstruction, such that the properties of each tier region 26, 28 and 30are distinctly different as a result of each tier region 26, 28 and 30having unique characteristics that differ from tier region to tierregion. More specifically, the tier regions 26, 28 and 30 can bearranged in such manner as to promote a synergistic energy absorptioneffect. In the illustrated example, the most compliant tier region 26forms an outermost surface 32 of the material 20 that will serve as thecontact surface of the material 20 or otherwise initially bear the loadapplied to the material 20, whereas the least compliant tier region 28defines the innermost surface 34 of the material 20 that is last to besubjected to the load applied to the material. The intermediate tierregion 30 has a compliance that is between those of the tier regions 26and 28. Ideally, as the most compliant tier region 26 saturates, thetier region 30 begins to deflect, and finally as the tier region 30saturates, the least compliant tier region 28 begins to deflect.

In FIG. 3, the tier regions 26, 28 and 30 are represented as differingon the basis of the number or size of their respective inclusions 24.Specifically, the embodiment on the left hand side of FIG. 3 ischaracterized by inclusions 24 that are of the same size (volume), butthe tier regions 26, 28 and 30 contain different numbers of theinclusions 24 (inclusions 24 per unit volume of the matrix 22). Moreparticularly, the number of inclusions 24 gradually decreases from thetier region 26 that forms the outer surface 32 of the material 20 towardthe tier region 28 that forms the opposite inner surface 34 of thematerial 20. In contrast, the embodiment on the right hand side of FIG.3 is characterized by the tier regions 26, 28 and 30 containing the samenumber of inclusions 24 (inclusions 24 per unit volume of the matrix22), but the tier regions 26, 28 and 30 contain inclusions 24 ofdifferent sizes (volumes). More particularly, the sizes of theinclusions 24 gradually decrease from the tier region 26 that forms thesurface 32 of the material 20 toward the tier region 28 that forms theopposite surface 34 of the material 20. In each tier region 26, 28 and30, the inclusions 24 are represented as being uniformly dispersed, inother words, the distances between immediately adjacent inclusions 24within a tier region 26, 28 or 30 are approximately the same.

Synergistic energy absorption exhibited by the impact-absorbingmaterials 20 can be represented by the force-deflection curve of FIG. 3,whereby the impact-absorbing materials 20 do not exhibit a singlesaturation level, but instead exhibit multiple minimized saturationlevels, such that the force-deflection plot tends toward a linearrelationship. As the impact-absorbing materials 20 are compressed, theymore gradually and more continuously stiffen to absorb more energy incomparison to the conventional foam material 10 of FIG. 1. As a result,the impact-absorbing materials 20 more efficiently absorb the load in amanner that will more safely protect a living body or inanimate objectprotected by the materials 20.

A wide variety of materials can be used as the matrices 22 of theimpact-absorbing materials 20, nonlimiting examples of which includepolymeric materials such as silicone, polycarbonate, polyurethane, foammaterials, natural and synthetic rubbers, polyethylene, ultra-highmolecular weight polyethylene, etc. In addition, it is foreseeable thatceramic, metallic, and metal matrix ceramic materials could be effectiveas the matrices 22, depending on the particular application. The sizesof the inclusions 24 are limited only by practical or process-relatedlimitations. Because the inclusions 24 may be voids or solids, theircommonality resides in their use to create a hierarchy of inclusions 24having different effects on the stiffness of their matrices 22 tosynergistically promote energy absorption within their matrices 22.Consequently, voids used as the inclusions 24 should vary in theirshapes, sizes (right hand side of FIG. 3) and/or number per unit volume(left hand side of FIG. 3) between the tier regions 26, 28 and 30 of thematerial 20. The voids may be present in the material 20 to result in anopen-cell or closed-cell configuration. If the inclusions 24 are in theform of solids, the solids can be formed from a wide variety ofmaterials or material combinations. In other words, all of the insertinclusions 24 in an impact-absorbing material 20 could have the verysame composition but differ in number per unit volume (left hand side ofFIG. 3) or size (right hand side of FIG. 3). As energy is absorbed bythe impact-absorbing material 20, the differing properties of theinclusions 24 are able to create different energy absorbing deformationsthat exhibit a gradual change of properties within the material 20. Aspreviously noted, such properties include the stiffness, elasticity,viscoelasticity, plasticity, and/or failure mode of the material 20.

Optionally, the sizes or numbers of the void inclusions may differ fromtier region to tier region on the basis of a geometric ratio, which maybe linear, exponential, etc. In this manner, the impact-absorbingmaterials 20 represented in FIG. 3 approach what may be termed afractal.

During investigations leading to the present invention, iterativemodeling of various impact-absorbing materials was completed, whichserved as the basis for the fabrication of test samples. During onephase of the investigation, force-deflection characteristics wereanalytically modeled for impact-absorbing materials represented in FIG.4. The material of FIG. 4A has tier regions 26, 28 and 30 that differ inboth number and size of void inclusions, such that the tier region 26 isthe most compliant and the tier region 28 is the least compliant as aresult of the relative size and number of their void inclusions. Thematerial of FIG. 4B is similar to FIG. 4A, but further incorporates voidinclusions into the tier region 26 that are of the same size as voidinclusions present in the intermediate tier region 30. The material ofFIG. 4C is similar to FIG. 4A, but further incorporates void inclusionsinto the tier region 26 that are of the same size as void inclusionspresent in the least compliant tier region 28.

For each configuration of impact-absorbing material in FIG. 4, anillustration is provided that represents the predicted model of thesynergistic energy absorption exhibited by the material duringcompression. The results from this phase of the investigation areplotted in the graph of FIG. 4. Generally speaking, as the porosityincreased, the critical buckling load decreased. Another effectivemeasure of the properties of the materials is to observe how the voidinclusions affect the strain energy density of the materials, which isessentially the amount of energy the materials absorb. Strain energyplots for the impact-absorbing materials in FIG. 4 are provided in FIG.5.

From the above investigations, it was concluded that as porosityincreases, strain energy density decreases. This conclusion suggestedthat simply increasing the number of void inclusions may not be optimalfor increasing the amount of energy absorbed by the impact-absorbingmaterial. During additional investigations, the void inclusions of FIGS.4A, 4B and 4C were modeled as containing water. The strain energydensities of the materials increased with increasing fluid-filled pores,suggesting that energy absorption may be more efficiently increased byinclusions that are filled with matter, for example, a solid or a liquid(such as a shear thickening fluid (STF)).

FIGS. 6 and 7 schematically represent two solid inclusions 24 thatcomprise a matrix 36 containing a dispersed phase 38. The insertinclusions 24 of FIGS. 6 and 7 differ by the size and amount of theirrespective dispersed phases 38. An impact-absorbing material havingsolid inclusions 24 of the types represented by FIGS. 6 and 7 has, ineffect, numerous and much smaller defects (the dispersed phases 38) thatcan take part in synergistic energy absorption. It is theorized that theinterfaces between the dispersed phases 38 and their matrix 36 arecapable of dissipating much greater amounts of energy, and thusamplifying the energy-absorption capability of the material 20.

The energy absorption capability of the solid inclusions 24 is believedto depend in part on the material of the matrix 36, the material andsize of the dispersed phase 38, the concentration of the dispersed phase38, etc. Suitable but nonlimiting examples of materials for the insertmatrix 36 include those previously noted for the matrix 22 of theimpact-absorbing material 20, a notable example of which is silicone orsome other elastomeric polymer. Graphite is a particularly suitable butnonlimiting example of a material for the dispersed phase 38. Thedispersed phase 38 may comprise nano-sized and/or micro-sized particles,though larger particle sizes are also possible. In addition, the use ofa dispersed phase 38 having a distribution of sizes within the solidinclusions 24 may be advantageous, for example, to dissipate energy atdifferent wavelengths.

FIGS. 8 through 17 depict additional embodiments of impact-absorbingmaterials that contain solid inclusions 24, for example, of the typerepresented in FIGS. 6 and 7. In these figures, consistent referencenumbers are used to identify the same or functionally equivalentelements, for example, the matrix 22, inclusions 24, tier regions 26, 28and 30, and surfaces 32 and 34 of the materials 20. In view ofsimilarities between the embodiments of FIGS. 3 through 5 and 8 through17, the following discussion of FIGS. 8 through 17 will focus primarilyon aspects that differ from the embodiment of FIGS. 3 through 5 in somenotable or significant manner. Other aspects not discussed in any detailcan be, in terms of structure, function, materials, etc., essentially aswas described for the first embodiment.

The impact-absorbing materials 20 of FIGS. 8 through 17 are believed tobe candidates for high-impact applications, for example, armor, in viewof the ability of their matrices 36 and dispersed phases 38 to dissipategreater amounts of energy. In each of FIGS. 8 through 17, theimpact-absorbing material 20 contains sets of solid inclusions 24 indifferent tier regions 26, 28 and 30. However, it should be noted thatdiscrete tiers are not necessary, in that the desired functionallygraded characteristic resulting from the hierarchy of inclusions 24 canbe achieved with a substantially homogeneous matrix 22 in which theinclusions 24 continuously vary in size, quantity, shape and/orcomposition in a direction through (e.g., the thickness of) theimpact-absorbing material 20. In the embodiment of FIG. 8, the solidinclusions 24 are of equal size (volume) and uniformly dispersed in eachof the tier regions 26, 28 and 30. As such, differences in propertiesbetween the tier regions 26, 28 and 30 can be achieved through the useof solid inclusions 24 that differ in stiffness, elasticity,viscoelasticity, plasticity, and/or failure mode. In FIG. 9, differentproperties in the tier regions 26, 28 and 30 are achieved as a result ofthe regions 26, 28 and 30 containing solid inclusions 24 that differ innumber and size. In particular, the solid inclusions 24 decrease in sizeand number from the tier region 26 to the tier region 30, and finally tothe tier region 28. In FIG. 10, the tier regions 26 and 30 contain solidinclusions 24 of two different sizes. In FIG. 11, the solid inclusions24 of the tier regions 26, 28 and 30 are all the same size, but areformed of different materials so that the inclusions 24 areprogressively stiffer in the tier regions 30 and 28 than the precedingregions 26 and 28, respectively. FIGS. 12, 13 and 14 represent solidinclusions 24 having different shapes than those of FIGS. 8 through 11.In FIG. 12, different types (composition, shape, size, etc.) of solidinclusions 24 are uniformly dispersed in individual tier regions 26, 28and 30 of a matrix 22 formed of a single material or in discrete layersof matrices 22 that can be formed of the same of different materials,and in FIGS. 13 and 14 the inclusions 24 have oval and squarecross-sectional shapes.

Impact-absorbing material 20 of this invention can also incorporate areinforcement phase of particles, fibers and/or fabrics, as representedin FIGS. 15 through 17. For example, FIG. 15 represents reinforcementfibers 40 that are dispersed and randomly oriented in the matrix 22 ofthe impact-absorbing material 20 of FIG. 8, and FIGS. 16A-B and FIGS.17A-D represent continuous fibers 42 incorporated into the material 20.In FIG. 16A, parallel fibers 42 are woven to form a mesh or fabric,while in FIG. 16B the fibers 42 are not woven and sets of parallelfibers 42 have different orientations within the material 20. FIGS. 17Athrough D represent other fiber orientations that can be used, includingpurposely symmetrically misaligned patterns to help reinforce stressflows around certain features in the material 20, for example, holes(FIG. 17A), inclusions (FIG. 17B) and other anomalies, concentricaligned patterns such as circles (FIG. 17C), and spiral or helicalpatterns around certain features in the material 20, for example, holes,inclusions and other anomalies (FIG. 17D). Reinforcement phases ofparticles and/or fibers provide another way to achieve synergisticenergy absorption, particularly in the event of a fracture occurring inthe matrix 22 and/or the fibers 42. Notably, the fibers 42 are capableof absorbing more energy in the event of a fracture than underconditions where the fibers 42 simply deform but do not fracture. Fibers42 of different diameters are also contemplated. If fibers 42 next to afiber 42 that fractures have larger diameters than the fractured fiber42, the larger fibers 42 may deform to the extent that their stressessurpass the yield strength but not the ultimate yield strength of thefiber material, during which energy would be absorbed. Strain associatedwith such stress may also result in the larger fibers 42 being deformedto the extent that their diameters are locally reduced to somethingsimilar to the fiber 42 that fractured, such that a subsequent stresscycle would approximately be a repeat of the prior stress cycle, i.e.,the same energy absorbed through fiber breakage. This would allow thematerial to absorb the same amount of energy in a cyclic fashion ratherthan only being able to absorb a certain amount of energy once.

Consistent with known composite materials, the mechanical properties ofthe impact-absorbing material 20 can be modified, including the abilityto obtain different properties in different directions, through the useof reinforcement materials having certain compositions, lengths,diameters, densities within the matrix 22, and orientations and weaves(or lack of orientation) within the matrix 22, confining thereinforcement material to layers within the impact-absorbing material20, etc. Suitable but nonlimiting examples of materials for the fibers42 include those previously noted for the matrix 22 of theimpact-absorbing material 20.

To optimize the impact-absorbing materials 20 of FIGS. 8 through 17 asarmor capable of withstanding very large and/or high-velocity impacts,considerable compressive forces should be dissipated. The reinforcementmaterials represented in FIGS. 15 through 17 promote the ability of thematerials 20 to withstand tensile and shear forces that might otherwisecause separation of the materials 20 during a very large and/orhigh-velocity impact. The materials 20 of FIGS. 8 through 17 (as well asthose of FIGS. 3 through 5) can also benefit from being mounted orotherwise supported on a substrate capable of promoting the resistanceof the materials 20 to tensile forces.

In addition or as an alternative to a reinforcement phase, theimpact-absorbing materials 20 of the invention could contain otheradditives. For example, fibers or other types of filler materials couldbe incorporated into the matrix 22 to promote or inhibit various otherproperties, for example, heat transfer, wicking (moisture transport),fire resistance, water resistance, anti-microbial properties, etc.Furthermore, a solid phase of polymeric pellets, granules, etc., (notshown) could be admixed into an uncured polymer material that forms thematrix 22, and which when subjected to a specified wave energy, such asinfrared, ultraviolet, x-ray, etc., particles of the solid phase arecaused to bond to each other. In this manner, the matrix 22 couldcontain a cured polymer phase that is independent of the remainingpolymer used to form the balance of the matrix 22.

Various potential manufacturing methods exist by which theimpact-absorbing materials 20 can be produced. As previously noted, thetier regions 26, 28 and 30 could be individually fabricated and thenfused, cast, laminated or bonded together to form the materials 20.Another option for tier regions 26, 28 and 30 defined within acontinuous matrix 22 is to fabricate the material 20 using processesthat rely on gravity to cause the inclusions 24 to settle and becomemore concentrated in the lower tier regions 28 and 30 during curing ofthe matrix 22. With this approach, visually discrete tiers may not bepresent, and instead the inclusions 24 may continuously vary in size,quantity, shape and/or composition in a direction through (e.g., thethickness of) the matrix 22 to achieve a desired functionally gradedcharacteristic for the impact-absorbing material 20. Slight deviations,both intentional and unintentional, in the distribution or arrangementof the inclusions 24 within the matrix 22 can be tolerated and stillobtain a functionally graded characteristic with the hierarchy ofinclusions 24.

Various applications for the impact-absorbing materials 20 of FIGS. 3through 5 and 8 through 17 exist, some of which are represented in FIGS.18 through 23. In FIGS. 18 and 19, multiple individual units ofimpact-absorbing materials 20 are represented as being discretelyincorporated into an American football helmet and an athletic shoe. InFIG. 20, multiple individual units of impact-absorbing materials 20 arerepresented as being incorporated into a mat, for example, a wrestlingmat, anti-fatigue floor mat, wall pad, gymnastics mat, etc.Impact-absorbing materials 20 of this invention can also be used toentirely (or nearly entirely) form articles, for example, a shin-guard(FIG. 21) for use in soccer, prosthetic sockets (FIG. 22), andwheelchair seats (FIG. 23). In each of these examples, theimpact-absorbing materials can be mounted or otherwise supported by ashell or backing material capable of promoting the resistance of thematerials 20 to tensile forces. Packaging for microelectronic devices isanother useful application, particularly for devices that aresusceptible to damage from physical shocks. Numerous other potentialapplications exist, including various other types of helmets (military,motorcycle, hockey, bicycle, etc.), other types of protective athleticequipment (knee pads, hockey/football pads, mouth guards, baseballgloves inserts, softball/baseball sliders, etc.), surfaces of passengervehicles (coverings for dashes, steering wheels, fronts and backs of busseats, bicycle seats, undercarriage armoring of military vehicles,etc.), residential and commercial floors, durable medical equipment (aircasts, braces, gurneys, crutches, helmets), apparel (for example,cycling shorts), etc.

From the foregoing, it should be appreciated that various factors willaffect the overall response of an impact-absorbing material 20 of thisinvention, and a structure into which the material 20 is incorporated.Such factors include:

-   -   Surface area of void inclusions 24 relative to volume (one type        of surface area to volume ratio);    -   Surface area of solid inclusions 24 relative to volume (another        type of surface area to volume ratio);    -   Geometry of inclusions 24 (elliptical, circular, rectangular are        some non-limiting examples);    -   Properties of the matrix material 22 (which could also vary with        depth or regionally).    -   Properties of the inclusions 24 (which could also vary with        depth or regionally).    -   Directionality resulting from orientations of the fibers 42.        Small-scale fibers 42 can disrupt blast waves, and larger fibers        (cylinders, rods, or more complicated cross sections) can resist        impact loads.    -   Hollow fibers 42 can perform similar functions with minimal        mass.    -   Hollow inclusions 24 might contain a matrix of stiff or brittle        material that encircles a pore, providing a lighter overall        material, but one that deforms or fails in a very specific way.    -   Inclusions 24 and fibers 42 can be tailored to fracture or        break, for example, to mitigate blast waves as a result of        property changes that occur after the inclusions 24 or fibers 42        are broken. It is possible to have a range of fiber sizes or        design fibers to fail at a range of loads/energies in order to        control the sequence of failure within the microstructure.    -   Dielectric materials can be used for the matrix material 22,        inclusions 24, and/or fibers 42 to provide information about the        integrity of the material 20.    -   Interface properties within the material 20 and between the        material 20 and surrounding structures.    -   Modulus ratio between the matrix material 22 and inclusions 24,        as well as a Poisson effects.

Yet another embodiment of the present invention pertains to animpact-mitigating compound 120. In some embodiments, compound 120 isprepared generally in accordance with a process 100 characterized inFIG. 24.

In the discussion that follows, reference is made to the various acts orsteps of a one-hundred series method as shown in FIG. 24. It isunderstood that such numbering of acts or steps is not to be confusedwith element numbering used elsewhere in this document. Further, thisdocument refers to characteristic dimensions of features. Generally,such characteristic dimensions are useful in broadly classifying thesize and/or shape of a feature. Non-limiting examples of characteristicdimensions include a diameter for a spherical shape, thickness and/orlength for solid particulate matter such as flakes, and thickness and/orlength for strut-shaped features. Typically, most of the characteristicdimensions used with relation to voids and inclusions refer broadly tosome form of spherical approximation.

Process 100 includes preparing 110 a mold in which uncured compound willbe placed, and a cured final material 120 produced. Preferably, the moldincludes one or more larger-scale features the imprint of which (eitherembossed as a void extending into the material or debossed as a raisedgeometric shape extending outwardly from the surface of the final curedcompound). In some embodiments, these larger-scale features havecharacteristic dimensions roughly in the centimeter range. However, itwill also be appreciated that in some other embodiments thecharacteristic dimension of the larger-scale features are established inrelation to a size range for the intermediate-scale features (such asbeing at least a whole number ratio larger, or an order of magnitudelarger, as examples). Further, in some embodiments, the shape of thelarger-scale features is selected to not include stress-inducing aspectssuch as sharp corners. Preferably, the shape of the features isgenerally smooth, such as all or part of a sphere, smooth cylinder, orelapse-type shape, as non-limiting examples.

Method 100 further includes activating 121 the polymerization process ofthe material to be molded. In some embodiments, the material mixedtogether is a two-part room temperature vulcanizing (RTV) siliconerubber material. The mixing of the two parts begins the polymerizationand cross-linking of the silicone rubber molecules. However, yet othermaterials are contemplated by other embodiments of the presentinvention. One such example includes the use of a single-part RTVcompound. Yet other examples include the use of any uncured,non-polymerized, or non-vulcanized material, as examples.

In some embodiments, method 100 further includes diluting 130 thepolymer compound, preferably after the polymerization or curing processhas begun. Such dilution can be used to affect the hardness of the curedproduct, and in so doing likewise affects the ability of the finalcompound to absorb strain energy. In some embodiments, it is preferredto add between about 10 percent to 40 percent by weight of diluent tothe activated (curing) material).

In yet other embodiments of the present invention an immiscible,volatile, and low-viscosity organic fluid such as DMSO or acetone isadded to the uncured polymer compound. This fluid creates voids in thepolymer, and in some embodiments creates voids that are larger than thevoids created during the application 170 of subatmospheric pressure. Insuch embodiments, the curing polymer may not be exposed tosubatmospheric pressure during curing, such that the polymer materialforms around the organic fluid droplets. After full curing of thepolymer, the organic fluid is removed by evaporation, which can be aidedby application of a vacuum to the cured material.

Some embodiments further include adding 140 particulate matter to thecuring compound. In one embodiment, graphite flakes are added to thepolymerizing material. As non-limiting examples, various embodiments ofthe present invention include the addition of (as referred to atwww.graphitestore.com) Microfyne graphite (approx. 325 mesh); #2 MediumFlake (approx. 200 mesh); and #1 Large Flake (approx. 50 mesh).Generally, these mesh sizes correspond to particle diameters of about40-50 microns, 70-80 microns, and 290-310 microns, respectively. In oneembodiment, the present invention contemplates the addition of fromabout 0.5 percent to about 1 percent (by weight) particulate matter,such as graphite, to the curing material. However, various otherembodiments contemplate the addition from about 0.2 percent to about 5percent by weight.

Method 100 further includes placing 150 the curing mixed material intothe mold. In some embodiments, the method further includes permitting160 the polymerization process to continue at substantially ambientpressure. In such embodiments, there is no attempt to apply a partialvacuum to the curing material during the earliest stages of curingactivity. Instead, various embodiments contemplate the curing of themixed material at substantially ambient pressure for at least about 5minutes. In some embodiments, this period of initial polymerization isallowed to continue for 10 minutes, and in yet other embodiments for 20minutes. During this initial period, polymerization and cross-linking ofthe mixed material begins and continues.

Method 100 further includes applying 170 a subatmospheric pressure tothe material in the mold cavity. In some embodiments, the application ofsubatmospheric pressure encourages the material to foam, withoutsubstantially letting any entrapped gases escape. However, in yet otherembodiments, the present invention contemplates the introduction ofsmall amounts of gas from the mold cavity into the curing material whilethe subatmospheric conditions are maintained on top of the curingmaterial. In such embodiments, this gas reintroduced into the materialthrough the mold cavity replaces any gas that was inadvertently removed,such as by application of excessive vacuum, or application of vacuumbefore significant cross-linking has occurred. Preferably, thesubatmospheric conditions are exposed to the curing material for theremainder of the cure cycle (such as for several hours).

After the material is cured, the vacuum is removed, at which time it ispossible that the final, cured compound reduces in height. The compoundis removed from the mold, and used as desired in any impact-mitigatingmanner, including the various application described herein.

FIG. 25 is a photographic representation of two sections of a material120 processed in accordance with portions of method 100. It can be seenthat the section of material shown on the left has the mold side 132facing upward, with various semi-spherical features 125 embossed on thatside. The sample of material on the right side of FIG. 25 shows the freeside (the side exposed to subatmospheric conditions) 134 facing upward.It can be seen on the sides of the material that method 100 has resultedin the introduction of various intermediate-scale features 127 withinthe volume of the cured final compound. Graphite flakes are not shown inFIG. 25.

FIG. 26 represents a generalized stress-strain (or load displacement)curve for a compound 120 according to one embodiment of the presentinvention. It can be seen that inventive materials in some embodimentsinclude small-scale features A, intermediate-scale features B, andlarge-scale features C distributed within a matrix, preferably a matrixof resilient material, and in some embodiments a matrix of anelastomeric material. In some embodiments, large-scale features Cinclude features having a characteristic dimension from about one-halfcentimeter to about two centimeters. These features can be of any type,including inclusions of particulate material or voids (including thosevoids created by the removal of particulate material such as cornstarch, salt, or other dissolvable substances). These relatively largefeatures exhibit behavior in two regions denoted by the “C” of FIG. 26.The first region includes a region in which an increase in load resultsin an increase in displacement. However, as previously discussed herein,the resilient material proximate to the features C deform (includingboth elastic and inelastic deformations, examples of which includebuckling, shearing, and compressive and tensile failures) as the loadincreases, such that a relatively larger degree of displacement isobtained with little or no increase in load. This is depicted as thegenerally flattened horizontal section of curve C.

However, compounds according to some embodiments of the presentinvention further include a distribution of intermediate-scale featureswithin the resilient matrix. As the deformation continues proximate tothe C features, the smaller B features induce larger stresses proximateto the B features, and the material proximate to the B features in roughproportion to the load. This portion of curve B is depicted within rangeD on FIG. 26. This D region can be considered as the handing-off ofstresses from the continued deformation and compaction proximate to theC features, and onto the elastic region D proximate to the B features.However, the stresses proximate to the B features reach a point at whichdeformation occurs in the matrix material proximate to the B features.This region is denoted by range E of FIG. 26. Within this range verysmall changes in load result in large changes in displacement.

Compound 120 further includes a third set of features A that are smallerin size than either of the C or B features. It can be seen that therange denoted “A” of FIG. 26 shows a region similar to the C and Bregions, yet occurring at still higher levels of stress. In someembodiments, the A features include micron range particulate matter,including as one example graphite flakes. The material proximate tothese micron-range features are generally the last to buckle within thecompound 120. In some embodiments, the B features are preferablyfeatures that are introduced into the compound during the cure cycle,although various other embodiments are not so constrained. In suchembodiments, the parameters of the curing cycle (such as cross-linkingtime prior to vacuum, level of vacuum, amount of dilution, etc.) resultin the introduction of intermediate-scale features 127, such as thoseseen in FIG. 25. In some embodiments, the size range of the small-scalefeatures A are selected to be about one order of magnitude smaller thanthe average B size. In still further embodiments, the size range of theC features is selected to be about one order of magnitude larger thanthe B features. It is understood that in various embodiments the orderof magnitude relationship between classes of features is preferablygreater than about seven to one, and less than about twelve to one. Instill further embodiments the order of magnitude ranges from about eightto one to about twelve to one. In still further embodiments, the orderof magnitude ranges from about nine to one to about eleven to one.

Referring again to FIG. 26, the dotted line of curve F graphicallydepicts the stress-strain response of a resilient material having asingle size range of features within the material matrix. As thematerial proximate to these features collapses (such as by buckling;although other failure mechanisms including failure in shear, failure intension, or failure in compression), the material responds withsignificant increases in strain with relatively small increases instress. However, as the material approaches very high level of strain,the compaction of the material results in an increase in stress requiredfor any further increases in strain. In some embodiments, operation ofthe material near the far right hand side of curve F can result inpermanent deformation of the matrix material, such as by tearing of thematrix material. This response curve F also shows a relatively lowamount of absorbed strain energy (strain energy being the area under thestress-strain curve). In contrast, a material 120 according to someembodiments of the present invention would continue to absorb strainenergy in the area under curves B and A, and above curve F.

FIGS. 27 and 28 are graphic depictions of stress/strain characteristicsof compounds prepared according to yet other embodiments of the presentinvention. FIG. 27 includes a plot for a material 220 according to oneembodiment of the present invention. This material was 60 percentsilicone by weight, 40 percent graphite by weight, was diluted 40percent by weight, and the graphite particles were Large Flake. FIG. 28shows a response curve for a material 320 in which the compound was 60percent by weight silicone, 40 percent by weight graphite, diluted 80percent by weight, and the graphite particles were Large Flake.

Also shown on FIGS. 27 and 28 are the stress/strain response curves forthree commercially available materials (designated I, II, and III) usedto absorb impacts in helmets. These two figures also show vertical linesrepresenting stresses induced by 10 g, 60 g, 100 g, 150 g, and 300 gimpacts. It can be seen that materials 220 and 320 outperform the threecommercially available materials in terms of the absorbed strain energy(area under the curve).

A linear single degree-of-freedom system is chosen to model the dynamicproperties of the various materials. The system model consists of arigid mass mounted on top of a sample of material which is fixed on theopposite end (FIG. 4.1).

The foam material acts as a linear spring, with stiffness K, anddashpot, with damping coefficient C. The input to the system, F(t), isan impulse, which sets the system into transient motion. Depending onthe value of the damping ratio, ζ, the transient motion may beunderdamped, overdamped, or critically damped. A system that isunderdamped (0>ζ>1) will exhibit vibratory motion. A system that isoverdamped (ζ>1) will not exhibit vibratory motion, but instead motionsimilar to a step input. A critically damped system (ζ=1) lies on thethreshold between overdamped and underdamped systems.

The single degree of freedom system depicted in FIG. 4.1 is described bythe following equation of motion

$\begin{matrix}{{\sum f_{E_{1}}} = {{m\overset{¨}{x}} = {F - {C\overset{.}{x}} - {Kx}}}} & (9) \\{F = {{m\overset{¨}{x}} = {{C\overset{.}{x}} = {Kx}}}} & (10) \\{\frac{F}{m} = {\overset{¨}{x} = {{\frac{C}{m}\overset{.}{x}} = {\frac{K}{m}x}}}} & (11)\end{matrix}$which may be written as

$\begin{matrix}{{\frac{1}{m}F} = {\overset{¨}{x} + {2{\zeta\omega}_{n}\overset{.}{x}} + {\omega_{n}^{2}{x.}}}} & (12)\end{matrix}$

A single degree-of-freedom experimental set up is used to acquire theacceleration history of the rigid mass for the dynamic characterizationof all material samples The experimental setup consists of a rigid massfixed to the top of a material sample, whose opposite end is fixed to arigid base. The rigid mass is constrained to stable motion with minimalfriction in the negative E3 direction by means of four roller bearingsconnected to four posts attached to a fixed base (FIG. 4.3).

Two single-axis Kistler K-Beam accelerometers (Milano, Italy) are fixedon opposing corners of the top plate with natural bees wax. An impulseinput is provided by

an externally triggered piezoelectric gun (Piezotronics, Model 086B09).Both the accelerometers and the piezoelectric gun output an analogvoltage between ±5 volts to a National Instruments DAQ board. Thepiezoelectric gun outputs the magnitude of the input impulse. Theaccelerometers output the acceleration time history of the rigid mass.LabVIEW v8.3.5 (National Instruments, Austin, Tex.) is used to collectand store the data. The complete experimental setup may be seen below inFIG. 4.4.

Since the piezoelectric gun is externally triggered, the accelerationprofile data must be phase shifted, such that the damped naturalresponse of the material sample begins at the time that the impulsereturns to zero. Basic time domain techniques are used under a linearassumption to analyze the phase shifted acceleration profile, namely thelog-decrement method for determining the damped natural frequency,damping ratio, and natural frequency.

The log decrement method of parameter estimation uses exponentiallydecaying oscillation peaks within the decay envelope to determine thedamping ratio

$\begin{matrix}{\Delta = {\frac{1}{n}{\ln\left\lbrack \frac{y_{n} - y_{f}}{y_{n + 1} - y_{f}} \right\rbrack}}} & (15) \\{{\zeta = \frac{1}{\sqrt{\frac{4\pi^{2}}{\Delta^{2}} + 1}}},} & (16)\end{matrix}$where n corresponds to the n^(th) peak of the oscillation decay. Thedamped natural frequency is determined using the time period ofoscillations

$\begin{matrix}{\omega_{d} = \frac{2\pi}{T_{d}}} & (17)\end{matrix}$and the natural frequency is then given by

$\begin{matrix}{\omega_{n} = {\frac{\omega_{d}}{\sqrt{1 - \zeta^{2}}}.}} & (18)\end{matrix}$Therefore, the second order system is defined by the natural frequencyof oscillation, ω_(n) and the damping ratio, ζ. These quantities areused directly to determine an estimate for the damping coefficient byrearranging Equation 15 to achieve the following relation:C=2ζω_(n) m.  (19)

Another method of determining the natural frequency of the system is byusing frequency domain techniques. In this case, an analysis of theenergy spectral density is appropriate to account for inconsistency ofsampling rate within a given sampling window. Energy spectral densitydirectly follows from Parseval's Theorem, which states that the sum ofthe square of a function is equal to the sum of the square of itstransform. The squared sum of the transform is called the energy densityspectrum, which describes the average distribution of signal energyacross frequency as given by

$\begin{matrix}{E = {{\overset{\infty}{\sum\limits_{- \infty}}{x_{n}}^{2}} = {\frac{1}{2\pi}{\int_{- \pi}^{\pi}{{{X({j\omega})}}^{2}{{\mathbb{d}\omega}.}}}}}} & (20)\end{matrix}$An energy spectral density plot represents the energy contained withinsignal at a specific frequency. The shape of an energy spectral densityplot for a second order system is identical to the shape of thefrequency response function. As with the frequency response function,the frequency corresponding to the peak magnitude value is the naturalfrequency.

For each sample, the energy spectral density is computed by taking thediscrete Fourier transform at n sampling intervals and squaring theresult respectively:X _(k) =DFT{x(nΔ)}  (21)X(f)|_(f=f) _(k) ≈ΔX _(k)  (22)E=|X _(f)|²=Δ² |X _(k)|².  (23)The natural frequency is determined by mapping the location of the peakmagnitude. This serves as s verification of the time domain estimationof natural frequency. A statistical analysis was completed usinganalysis of variance (ANOVA) Student Newman-Keuls post hoc tests at asignificant level of 5%. All statistical tests were performed usingStatView (SAS Institute, Cary, N.C.).

Natural frequency is determined using both time domain and frequencydomain analysis for verification. In all pure silicone cases, thepercent error between the two different calculations methods is lessthan 2%, so the values found using the time domain technique arereported. The energy spectral density may be found is FIG. 4.5.

The natural frequency of Si₄₀ and Si₈₀ is 69.21±1.08 rad/s and56.34±1.31 rad/s, respectively. The damping coefficient of Si₄₀ and Si₈₀is 17.69±2.28 Ns/m and 24.71±3.99 Ns/m, respectively. Pure siliconesamples have a unique acceleration profile, characterized by significantdamping and minimization of peak amplitude, especially when compared toMaterial I and Material II materials (FIG. 4.6).

Si₄₀ and Si₈₀ are statistically significant with respect to both naturalfrequency and damping coefficient. The pure silicone samples exhibit anegative correlation between natural frequency and thinning percentageof silicone; whereas, a positive correlation exists between dampingcoefficient and thinning percentage of silicone (FIG. 4.7 and FIG. 4.8).

Natural frequency is determined using both time domain and frequencydomain for verification. In all Microfyne cases, the percent errorbetween the two different calculations methods is less than 7%, so thevalues found using the time domain technique are reported (Table 4.1).The energy spectral density may be found in FIG. 4.9. Both naturalfrequency and damping coefficient are higher than those found for puresilicone. The acceleration profile for Si₄₀ samples has a higher peakmagnitude and more oscillations than the pure silicone samples. The peakmagnitude seems to increase with the addition of more graphite. Theacceleration profile for Si80 samples, characterized by lower peakamplitude and a longer time period of oscillation is more similar to thepure silicone samples. As with the Si₄₀ samples, the peak magnitudeincreases with increasing graphite content (FIG. 4.10).

TABLE 4.1 Quantitative calibration results for natural frequency anddamping coefficient of Microfyne series samples. Natural FrequencyDamping Coefficient (rad/s) (Ns/m) 70Si₄₀30G_(MF) 99.71 2.55 45.20 ±7.67 60Si₄₀40G_(MF) 116.56 ± 3.53 58.58 ± 6.53 70Si₈₀30G_(MF)  85.64 ±6.94 45.19 ± 9.13 60Si₈₀40G_(MF) 100.97 ± 9.63  59.25 ± 15.07

All Microfyne series samples were statistically significant with respectto natural frequency, except 70Si₄₀30G_(MF) and 60Si₈₀40G_(MF). In allMicrofyne series samples, natural frequency and damping coefficient arepositively correlated with volume of impregnated graphite (FIG. 4.11 andFIG. 4.12).

Natural frequency is determined using both time domain and frequencydomain for verification. In all #2 Medium Flake cases, the percent errorbetween the two different calculations methods is less than 10%, so thevalues found using the time domain technique are reported (Table ##).The energy spectral density may be found in FIG. 4.13. The impulseresponse of the #2 Medium Flake series samples are all very similar withnoted mitigation of the peak amplitude followed by damped oscillation.

TABLE 4.2 Quantitative calibration results for natural frequency anddamping coefficient of #2 Medium Flake series samples. Natural FrequencyDamping Coefficient (rad/s) (Ns/m) 70Si₄₀30G_(#2) 119.19 ± 3.70  50.07 ±11.94 60Si₄₀40G_(#2)  114.9 ± 4.05 45.56 ± 3.41 70Si₈₀30G_(#2)  97.18 ±2.34 33.59 ± 4.05 60Si₈₀40G_(#2) 106.23 ± 4.08 49.16 ± 5.59

All #2 Medium Flake series samples were statistically significant withrespect to natural frequency. Natural frequency and damping coefficientfor the Si₄₀ samples both have a negative correlation with volumefaction of graphite. This is the first incidence of a negativecorrelation in graphite impregnated samples. Natural frequency anddamping coefficient for the Si₈₀ samples both have a positivecorrelation with volume fraction of impregnated graphite (FIG. 4.15 andFIG. 4.16).

Natural frequency is determined using both time domain and frequencydomain for verification. In all #1 Large Flake cases, the percent errorbetween the two different calculations methods is less than 11%, so thevalues found using the time domain technique are reported (Table ##).The energy spectral density may be found in FIG. 4.17. The impulseresponse of the #1 Large Flake series samples has even further mitigatedpeak amplitudes than the #2 Medium Flake series, followed by smooth,slow damped oscillation (FIG. 4.18).

TABLE 4.3 Quantitative calibration results for natural frequency anddamping coefficient of #1 Large Flake series samples. Natural FrequencyDamping Coefficient (rad/s) (Ns/m) 70Si₄₀30G_(#1) 115.60 ± 9.85 43.75 ±4.63 60Si₄₀40G_(#1) 123.34 ± 4.31  56.04 ± 11.53 70Si₈₀30G_(#1)  91.65 ±2.63 31.31 ± 2.77 60Si₈₀40G_(#1) 100.81 ± 1.95 42.90 ± 6.17

All #1 Large Flake series samples were statistically significant withrespect to natural frequency. Natural frequency and damping coefficientfor both Si₄₀ and Si₈₀ samples have a positive correlation with volumefraction of impregnated graphite (FIG. 4.19 and FIG. 4.20).

Natural frequency is determined using both time domain and frequencydomain for verification. In each of the All series cases, the percenterror between the two different calculations methods is less than 9%, sothe values found using the time domain technique are reported (Table4.4). Energy spectral density may be found in FIG. 4.21. The impulseresponse of Si₄₀ samples has returned to the acceleration profile of theMicrofyne series samples, characterized by a high peak magnitude,followed by a series of damped oscillations. The impulse response of theSi₈₀ samples is characterized by a low peak magnitude followed by aseries of damped oscillations (FIG. 4.22).

TABLE 4.4 Quantitative calibration results for natural frequency anddamping coefficient of All series samples. Natural Frequency DampingCoefficient (rad/s) (Ns/m) 70Si₄₀30G_(ALL) 125.35 ± 8.65  53.83 ± 13.5060Si₄₀40G_(ALL) 125.56 ± 7.56 61.09 ± 7.84 70Si₈₀30G_(ALL)  91.39 ± 2.6436.85 ± 3.69 60Si₈₀40G_(ALL) 104.10 ± .67  51.16 ± 6.10

Each of the All series samples are statistically significant withrespect to natural frequency, except 70Si₄₀30G_(All) to 60Si₄₀40G_(All)and 70Si₇₀30G_(All) to 60Si₈₀40G_(All). Natural frequency and dampingcoefficient for both Si₄₀ and Si₈₀ samples have a positive correlationwith volume fraction of impregnated graphite (FIG. 4.23 and FIG. 4.24).The damping coefficient is more sensitive than the natural frequency forboth Si₄₀ and Si₈₀ samples.

Natural frequency (ωn) and damping coefficient (C) are defined for alleighteen different material samples using a linear singledegree-of-freedom model. Each material has a distinctly lineardeformation region for low strain values. Due to the nature of thedynamic impulse test, the deformations are small and likely to remainwithin the linear range of deformation. This can be verified by plottingthe acceleration of the peaks within the damping envelope against timeon a log-log plot and checking for a linear relationship. For themajority of materials, a linear relationship existed between theacceleration of the peaks and time. For materials that reach non-lineardeformation ranges during dynamic testing, the assumption of a linearsystem offers a decent approximation of natural frequency and dampingcoefficient, but could be refined by accounting for non-linearities.

Acceleration profile plots are generated to compare the performance ofpure silicone and graphite impregnated samples with Material I, MaterialII, and Material III helmets. The impulse input is slightly different(±500N) for each sample due to physical system limitations, so it isbest to compare the basic shape of the plot as opposed to specificmagnitude values.

The pure silicone samples may be thinned up to 90% by weight to achieveincreasingly compliant material properties. Natural frequency isnegatively correlated with thinning percentage of silicone; whereas,damping coefficient is positively correlated with thinning percentage ofsilicone. The acceleration profile of the pure silicone samples ischaracterized by a low peak magnitude follow by several long time periodoscillations. The time period of oscillation for both pure siliconesamples is greater than Material I, Material II, and Material III. Thepure silicone samples are most comparable to the Material III material,with relatively low natural frequency and low damping ratio. Both Si₄₀and Si₈₀ have significantly lower peak magnitudes than both the MaterialI and Material II.

The addition of Microfyne graphite to the silicone allows for thevariation of both natural frequency and damping coefficient, whichdrastically changes the acceleration profile. A positive correlationbetween damping coefficient and graphite content exists, but unlike inthe pure silicone samples, natural frequency has a negative correlationwith graphite content. The acceleration profile of the Microfyne seriessamples has a smaller time period of oscillation, which leads to higherpeak magnitudes and more oscillations. The response of the70Si₈₀30G_(MF) sample is identical to the Material III response. Thepeak magnitudes for 70Si₄₀30G_(MF) and 70Si₈₀30G_(MF) are much lowerthan both the Material I and Material II. The peak magnitudes of60Si₄₀G_(MF) and 60Si₈₀40G_(MF) are comparable to the Material I andMaterial II.

The addition of #2 Medium Flake graphite to the silicone allows forvariation of both natural frequency and damping coefficient, andtherefore control of the acceleration profile. The Si₄₀ samples have anegative correlation between both natural frequency and dampingcoefficient and graphite content; whereas, the Si₈₀ samples have apositive correlation between natural frequency and damping coefficientand graphite content. Microfyne impregnated graphite samples are theonly samples that have different correlations between Si₄₀ and Si₈₀samples. In all cases, the peak amplitude is well below that of MaterialI and Material II, but higher than that of the Material III. Generally,the Si₈₀ samples have lower peak amplitude than the Si₄₀ samples, butSi₄₀ samples damp faster.

The addition of #1 Large Flake graphite to the silicone allows forvariation of both natural frequency and damping coefficient, andtherefore control of the acceleration profile. Natural frequency anddamping coefficient are both positively correlated with graphitecontent. All peak amplitudes are generally well below Material I andMaterial II and below or comparable to Material III. The Si₄₀ samplestend to damp faster than the Si₈₀ samples and the Si₈₀ samples have alonger time period of oscillation than the Si₄₀ series.

The addition of an equal weight percentage of each type of graphiteparticle to the silicone allows for variation of both natural frequencyand damping coefficient, and therefore the control of the accelerationprofile. Natural frequency and damping coefficient are both positivelycorrelated with graphite content. All peak amplitudes are generally wellbelow Material I and Material II. Only the Si₈₀ series peak amplitudesare below those of Material III.

Across all groups, natural frequency and damping coefficient are bothvery sensitive to changes in volume fraction of impregnated graphite;neither one nor the other parameter seems to dominate. Generallyspeaking, the Si₄₀ samples have an acceleration profile similar to theMaterial I and Material II; whereas, the Si₈₀ series samples have anacceleration profile similar to the Material III. Increasing graphitesize has a distinct effect on the magnitude of the peak amplitude. Thelarger the size of the particle inclusion, the lower the peak amplitude.The samples with an equal weight percentage of graphite return toacceleration profile characteristics similar to the Microfyne seriessamples. This suggests that the material behavior is dominated by thesmallest particle inclusion, which is consistent with the quasi-staticparameters and compressive stress-strain deformation.

Si₈₀ graphite impregnated silicone displays superior dynamic propertieswhen compared to Material I, Material II, and Material III paddingmaterials. In all cases, the peak amplitude of the silicone and graphiteimpregnated silicone was equivalent or below that of Material I andMaterial II. The peak amplitudes of Si₈₀ series samples were generallybelow or equivalent to Material III padding. With the addition ofgraphite to silicone, the natural frequency, damping coefficient, andtherefore the acceleration profile may be tuned to specific impactloading conditions.

In the case of football helmets, the dynamic loading conditions may bedescribed by defining a realistic bound for the natural frequency basedon the natural frequency of the head and the natural frequencies of atypical impact. Generally speaking, the ideal material would havedynamic properties whose natural frequency is distinctly different fromthe natural frequencies of the human head and helmet impacts.

Dynamic properties of helmet impacts are poorly defined, with limitedexperimentally obtained and computationally verified research of thenatural frequency of an impact. Newman et al. report frequencies forhelmet-to-helmet impacts near 1875 Hz and 3202 Hz. Therefore, an idealpadding material should remain below frequencies about 1000 Hz.

Based on the available estimations of natural frequency, it seemsreasonable to require that the natural frequency of the padding materialstay well below 300 Hz, the lowest reported natural frequency. However,the whole human body has a natural frequency below 10 Hz so the naturalfrequency of the padding material should be reasonably higher than 10Hz. Combining the two design constraints means that the padding materialmust be between 10 Hz and 300 Hz. A proposed ideal natural frequencythat falls within this range is a moderate 100 Hz. With an understandingof the limitations of natural frequency, a brief analysis of the shockspectrum of a helmet impact may be completed to determine an upper boundon the desired linear spring constant. The range of acceptable springconstant values will vary depending on the parameters of each specificimpact loading condition, and therefore, must be evaluable oncase-by-case scenario. Ultimately, multiple graphite impregnatedsilicone samples have a natural frequency near 100 Hz and the linearspring stiffness, which is directly related to the shear modulus, may becustomized to meet impact loading condition demands.

At a micro-scale level, the addition of graphite or other particles tosilicone or other elastomaterial is one method of altering the materialproperties by means of intentional variation in material properties andgeometry. This proved to be an effective method for tuning thequasi-static and dynamic properties of graphite impregnated silicone.This methodology can be extended to materials at a macro-scale level, inwhich materials of varying properties are layered with intentionalisotropic or anisotropic geometries to improve and control energyabsorption capabilities. The comments that follow pertain to FIGS. 5.1,5.2, 5.3, 5.4, 5.5, and 5.6.

The addition of materials of varying property to a specific materialgeometry is thought to effectively act as a multiple mass-spring-dampersystem, in which each layer is characterized by a different stiffnessand damping value. This can also be thought of in terms of filtering, inwhich each material included in the geometry is designed to filterspecific frequencies. For example, a compliant material would mitigatelow-frequency impacts; whereas, a stiff material would mitigatehigh-frequency impacts. Strain energy is a commonly accepted way ofquantifying the energy absorption of a material.

A 30 cm by 30 cm block of unit depth is taken as a base geometry foreach geometrical configuration of the material. Inclusions are added tothe base geometry and allowed to vary in size, number, and shape. Thisultimately resulted in twelve geometries of interest (FIG. 5.2). Fornotation, the inner geometry, referred to as inclusions, is surroundedby the outer material, and referred to as the matrix material.

Both the matrix material and inclusion material properties are allowedto vary, resulting in a non-repeating permutation of material propertysets. The values for shear modulus (μ) and bulk modulus (κ) for eachsilicone and graphite impregnated silicone sample are used as materialparameters. In order to minimize computation time of the permutation, arange of experimentally obtained properties is selected; with theknowledge that any one of the sets of parameters may be achieved withappropriate thinning percentage of silicone and graphite content (Table5.1).

TABLE 5.1 Representative range of pure silicone and graphite impregnatedsilicone Material μ(Pa) K (Pa) 1 40000 15200 2 25000 90000 3 14500 400004 9000 42500

The geometry versions are modeled in COMSOL v3.2 and the iteration iscompleted using a MATLAB algorithm. A static linear analysis of thematerial for a 3000 N distributed load (stress) input is computed. Theload is representative of approximate loading conditions in a 50 gfootball impact. Outputs of the program are contribution to strainenergy from the matrix material, inclusion material, and total strainenergy corresponding to each of the twelve permutation materialconfigurations.

There is a trend in the computation of strain energy, which in the caseof design, limits its effectiveness in characterizing energy-absorbingmaterial. Since strain energy is the integral of the stress-straincurve, its value is largely dependent on the shear modulus and bulkmodulus of the material. Strain energy can be computed and maximizedusing two different methods: strain input or load input, each having adifferent output. If the input is a strain level, the stiffest materialwill have the highest strain energy (FIG. 5.3); whereas, if the input isa stress level, the most compliant material will have the highest strainenergy (FIG. 5.4).

For this reason, a deformation filter is applied to the output data forwhich the desired range of deformation is appropriately selecteddepending on the energy-absorption application. The deformation filtereliminates flawed data in which one of the following occurs:

-   -   1. The highest strain energy output is due to an unreasonably        stiff material, in the case of a uniform strain input or    -   2. The highest strain energy output is due to an unreasonably        compliant material, in the case of a uniform stress input.        The deformation filter can be likened to a band-pass filter, in        which lower and upper deformation bounds are defined. The lower        bound ensures that Case 1 does not occur in which the material        is unreasonable stiff for the energy-absorption application. The        upper bound ensures that Case 2 does not occur, in which the        material is unreasonably compliant for the energy-absorption        application.

In preparing impact mitigating material bounds were set at 10% and 40%of initial height, such that materials whose final deformation fallsoutside of this range for the load input are discarded. Output wasconverted to strain energy density to normalize by volume. The series ofmodels with increasing diameter of cylindrical inclusions resulted inmaximum strain energy of 38.9 J/m³ (FIG. 5.5). The shear modulus andbulk modulus of the matrix and inclusion material corresponding tomaximum strain energy are given in Table 5.2. Both filtered andunfiltered results are shown in FIG. 5.5.

TABLE 5.2 Shear and bulk modulus corresponding to maximum strain energyof increasing inclusion diameter series. Shear Modulus (Pa) Bulk Modulus(Pa) Matrix 14500 40000 Inclusion 7500 40000

The series of models with increasing volume fraction of cylindricalinclusions resulted in maximum strain energy of 40.9 J/m³ (FIG. 5.6).The shear modulus and bulk modulus of the matrix and inclusion materialcorresponding to maximum strain energy are given in Table 5.3.

TABLE 5.3 Shear and bulk modulus corresponding to maximum strain energyof increasing volume fraction of cylindrical inclusions series. ShearModulus (Pa) Bulk Modulus (Pa) Matrix 14500 40000 Inclusion 7500 40000

The series of models with increasing volume fraction of ellipticinclusions resulted in maximum strain energy of 38.5 J/m³ (FIG. 5.7).The shear modulus and bulk modulus of the matrix and inclusion materialcorresponding to maximum strain energy are given in Table 5.4.

TABLE 5.4 Shear and bulk modulus corresponding to maximum strain energyof increasing volume fraction of elliptic inclusions series. ShearModulus (Pa) Bulk Modulus (Pa) Matrix 14500 40000 Inclusion 7500 40000

One configuration of material properties resulted in a moderatelycompliant matrix material (μ=14.5 kPa, κ=40 kPa) with a more compliantinclusion material (μ=7.5 kPa, κ=40 kPa). Geometry is shown to have anoticeable but relatively limited effect on maximum strain energy due todeformation limitations. Strain energy density can be sensitive tochanges in elliptic inclusions.

The shape of each correlation is similar, characterized by a rise to acritical strain energy value followed by decreasing strain energyvalues, and takes into account the deformation filter. As the diameteror volume fraction of inclusions increases, the maximum strain energyincreases. Since the input is a uniform stress, an increase in strainenergy density corresponds to increasingly compliant materials. Becauseof this, the strain energy reaches a critical point at which, if thematerial becomes any more compliant, the deformation will fall outsideof the upper deformation bound and therefore the material will bediscarded. The critical point is the maximum strain energy within agiven deformation range.

From an analysis of strain energy, a very useful fundamental trend isunderstood, in that the most compliant material has the highest strainenergy for a uniform stress input and the stiffest material has thehighest strain energy for a uniform strain input. This suggests that asuitable deformation range can be defined for the material depending onthe loading conditions and application.

For the case of football helmets, one design criterion is a minimumdeformation of 10% and a maximum deformation of 40%. A minimum of 10%deformation helps provide that the material is compliant as opposed to arigid, albeit high strain energy, material. A maximum of 40% deformationensures that the material has not reached its maximum deformationcapabilities. This means that the strain energy can be quantified up to40% deformation for a given stress, but in some impacts, the material isstill able to deform further to at least 80% of the initial height. Thisis helpful, as football impacts are regularly recorded above 100 g's,which requires extreme deformation for total energy-absorption.

X1. One embodiment of the present invention pertains to a compound forprotection of an object from a dynamic load, and includes a matrixmaterial including at least two sizes of stress-concentrating features,a plurality of first features having a first average characteristicdimension of between about ten microns and about two hundred microns,and a plurality of second features having a second averagecharacteristic dimension that is at least about one order of magnitudelarger than said first average characteristic dimension, wherein thematerial proximate to said first and second features progressivelybuckles upon application of the load, such that material proximate saidfeatures tends to structurally buckle before the buckling of materialproximate to said first features

X2. Yet another embodiment of the present invention pertains to acompound for protection of an object from a dynamic load, and includes aresilient matrix material including distributed therein a plurality offirst features, a plurality of second features, and a plurality of thirdfeatures, each of said first features, second features, and thirdfeatures being adapted and configured to concentrate stress in thematerial proximate to the corresponding said feature, wherein said firstfeatures have a first average characteristic dimension, said secondfeatures have a second average characteristic dimension, and said thirdfeatures have a third average characteristic dimension, the ratio of thesecond average dimension to the first average dimension is between aboutseven and twelve, and the ratio of the third average dimension to thesecond average dimension is between about seven and twelve, wherein saidmatrix material and said first, second, and third features are selectedsuch that the compound exhibits substantially elastic response to acompressive strain greater than about forty percent.

X3. Yet another embodiment of the present invention pertains to a methodof making a dynamic load-mitigating material, and includes providingfirst and second compounds that when combined form a silicone polymer,providing a plurality of separable particles each having acharacteristic dimension less than about three hundred microns, mixingthe first and second compounds and the particles, permitting the mixtureto polymerize for at least about five minutes, and then exposing themixture to pressure less than ambient pressure.

X4. Yet another embodiment of the present invention pertains to a methodof making a dynamic load-mitigating material for a helmet, and includesproviding a compound that is curable to form a polymer, providing a moldcavity having an internal height adapted and configured to produce curedsilicone of a thickness suitable for use in a helmet, placing thecompound in the mold cavity, curing the compound for a predeterminedperiod of time, and exposing the mixture in the mold cavity to pressureless than ambient pressure after said permitting.

X5. Yet another embodiment of the present invention pertains to a methodof making a dynamic load-mitigating material, and includes providingfirst and second compounds that when combined form a cross-linkablepolymer, providing a mold cavity including a plurality of surfacefeatures each having a characteristic dimension greater than about onehalf centimeter and less than about two centimeters, mixing the firstand second compounds and placing the mixture in the mold cavity,permitting the mixture to cross-link for at least about five minutes,and exposing the mixture in the mold cavity to pressure less thanambient pressure after said permitting.

Any of the preceding statements X1 through X5 wherein the deformation ofsaid material proximate to any of said features is substantiallyelastic, buckling.

Any of the preceding statements X1 through X5 wherein the deformation ofsaid material proximate to said third features is substantiallyinelastic shear, or compressive fracture, or tensile tearing.

Any of the preceding statements X1 through X5 wherein said secondfeatures are voids in said matrix material.

Any of the preceding statements X1 through X5 wherein said firstfeatures are graphite flakes.

Any of the preceding statements X1 through X5 wherein said thirdfeatures are pockets molded into the material.

Any of the preceding statements X1 through X5 wherein the ratio of thethird average dimension to the second average dimension is greater thanabout seven.

Any of the preceding statements X1 through X5 wherein the ratio of thesecond average dimension to the first average dimension is greater thanabout seven.

Any of the preceding statements X1 through X5 wherein said matrixmaterial is an elastomer or not a metal.

Any of the preceding statements X1 through X5 wherein the resilientmaterial has a Shore hardness of less than about 40 on the A scale.

Any of the preceding statements X1 through X5 wherein the material withfeatures exhibits substantially elastic response to a compressive straingreater than about sixty percent.

Any of the preceding statements X1 through X5 wherein the ratio of thesecond average dimension to the first average dimension is greater thanabout ten, and the ratio of the third average dimension to the secondaverage dimension is greater than about ten.

Any of the preceding statements X1 through X5 wherein the substance is apolymer, and the second features are voids in said substance formedduring polymerization.

Any of the preceding statements X1 through X5 wherein any of thefeatures comprise particulate matter, including graphite, corn starch,table salt, or any readily dissolvable solid that does not chemicallydegrade the matrix material.

Any of the preceding statements X1 through X5 wherein the voids areformed around particulate material during polymerization of said matrixmaterial, with the particulates being removed from the polymerizedmaterial.

Any of the preceding statements X1 through X5 wherein the featuresinclude solid matter that is water soluble, and the solid matter isremoved with water.

Any of the preceding statements X1 through X5 wherein during saidexposing the pressure is less than about half of ambient pressure.

Any of the preceding statements X1 through X5 wherein said permitting isfor at least about ten minutes, or at least about fifteen minutes.

Any of the preceding statements X1 through X5 wherein said mixingincludes a diluent.

Any of the preceding statements X1 through X5 wherein any one of thefeatures includes particles that have a mean characteristic length lessthan about one hundred and fifty microns and greater than about fiftymicrons and a standard deviation about the mean of less thanapproximately twenty microns.

Any of the preceding statements X1 through X5 wherein the first andsecond compounds have a first weight, the particles have a secondweight, and the second weight is less than about ten percent of thefirst weight.

Any of the preceding statements X1 through X5 wherein the thickness ofthe cured silicone is less than about three centimeters.

Any of the preceding statements X1 through X5 wherein the surfacefeatures are at least partially spherical.

In one alternative embodiment according to the present disclosure, anovel structure that can be utilized for blast mitigation and shockwavemitigation is disclosed. The blast/shockwave mitigation structure issimilar to the above-described impact absorbing material, however,different in at least one important manner. As described herein, theimpact absorbing material includes a matrix material which includes setsof load/stress-concentrating features. Each of the sets is about anorder of magnitude different in size than the others, with the smallestset being between about 10 and 100 microns. The material proximate toeach of the three sets of features progressively buckles uponapplication of a load, such that the material proximate to the largerset of features deforms prior to the material proximate to smaller setof features.

One difference between the blast/shockwave mitigation structure and theimpact absorbing structure described herein is that some or all of thefeatures of the sets of features described herein can be partially orfully filled with a fluid other than air. The fluid can be a combinationof water and/or oil. Other fluids with different levels of viscosity,e.g., uncured silicone, may be used as well.

To test the blast/shockwave structure, circular test structures wereproduced. These test structures 500 are depicted in FIG. 29. The teststructure 500 includes a top plate 502, a cylindrical blast/shockwavemitigation structure 504, a ring 506, and a bottom plate 508. The ring506 is configured to contain the blast/shockwave mitigation structure504 within the test structure during a blast test; however, it allowsthe structure 504 to deform.

The test structure 500 was used to test various embodiments of theblast/shockwave mitigation structure 504. In one case, variousinclusions present in the blast/shockwave mitigation structure 504 werefilled with water; in another case vegetable oil was used, and inanother case no filling was provided. The test structures were then usedin blast testing. The result of blast testing is provided below:

Average Peak Average Impulse Overpressure Mitigation Mitigation Padsfilled w/Water 55.66% 41.58% Pads filled w/V-Oil 64.78% 68.42% All Pad -No Fill 35.53% 51.05%

Another test was also performed without the blast/shockwave mitigationstructure 504 for reference. The results of the blast testing aredepicted in FIG. 30. Referring to FIG. 30, a plot of pressure vs. timeis depicted. Trace I depicts the test where no blast/shockwavemitigation structure 504 was used. As can be seen at about 1.15 ms thereis a sudden rise in the pressure that is translated from one of the topplate 502 or the bottom plate 508 to the other. After the sudden rise,trace I shows a gradual lowering of the pressure. Trace II depicts thetest where the blast/shockwave mitigation structure 504 is not filledwith any fluid. While the amplitude of pressure is lower than trace I, asimilar rise (i.e., differential of pressure vs. time) is seen in traceII just before about 1.3 ms. It should be appreciated that there is adelay of about 0.1 ms as compared to trace I. Trace III depicts the testwhere the blast/shockwave mitigation structure 504 is filled with water.Several observations are noteworthy. First, the change in pressure intrace III is unlike traces I or II. The rise is slower and the amplitudeis lower. Also, the delay is longer, about 0.15 ms as compared to traceI. Similarly, trace IV depicts the test where the blast/shockwavemitigation structure 504 is filled with vegetable oil. Again, the risein pressure in trace IV is slower and the amplitude is lower than therise and amplitudes of traces I, II, or III. There is also a longerdelay of as compared to trace I.

The above results clearly show that the blast/shockwave mitigationstructure described above can advantageously slow the progression of ashockwave and reduce its amplitude as well as lower the change ofpressure as a function of time.

Referring to FIG. 31, a block diagram representing a process forfabricating the blast/shockwave mitigation structure, according to oneprocessing embodiment is depicted. The process depicted in FIG. 31 issimilar to the process depicted in FIG. 24, with some differences thatare described below.

Process 600 includes preparing 610 a mold in which uncured compound willbe placed, and a cured final material 620 produced. The mold includesone or more larger-scale features the imprint of which result in largerscale voids within the final material. In some embodiments, theselarger-scale features have characteristic dimensions roughly in thecentimeter range. However, it will also be appreciated that in someother embodiments the characteristic dimension of the larger-scalefeatures are established in relation to a size range for theintermediate-scale features (such as being at least a whole number ratiolarger, or an order of magnitude larger, as examples). Depending on theshape of the mold and the shape of the features, it may be necessary tomake the material in portions and then fuse the portions together afterthe portions are removed from the mold, as is known to a person havingordinary skill in the art. Further, in some embodiments, the shape ofthe larger-scale features is selected to not include stress-inducingaspects such as sharp corners. Preferably, the shape of the features isgenerally smooth, such as all or part of a sphere, smooth cylinder, orelapse-type shape, as non-limiting examples. For the purpose of theprocess 600, these larger sized features are hereinafter referred to asgeometric features, as the location of these features are deterministicbased on the shape of the mold.

Process 600 further includes activating 621 the polymerization processof the material to be molded. In some embodiments, the material mixedtogether is a two-part room temperature vulcanizing (RTV) siliconerubber material. The mixing of the two parts begins the polymerizationand cross-linking of the silicone rubber molecules. However, yet othermaterials are contemplated by other embodiments of the presentinvention. One such example includes the use of a single-part RTVcompound. Yet other examples include the use of any uncured,non-polymerized, or non-vulcanized material, as examples.

In some embodiments, process 600 further includes diluting 630 thepolymer compound, preferably after the polymerization or curing processhas begun. Such dilution can be used to affect the hardness of the curedproduct, and in so doing likewise affects the ability of the finalcompound to absorb strain energy. In some embodiments, it is preferredto add between about 10 percent to 40 percent by weight of diluent tothe activated (curing) material).

In yet other embodiments of the present invention an immiscible,volatile, and low-viscosity organic fluid such as DMSO or acetone isadded to the uncured polymer compound. This fluid creates voids in thepolymer, and in some embodiments creates voids that are larger than thevoids created during the application 670 of subatmospheric pressure(described below). In such embodiments, the curing polymer may not beexposed to subatmospheric pressure during curing, such that the polymermaterial forms around the organic fluid droplets. After full curing ofthe polymer, the organic fluid is removed by evaporation, which can beaided by application of a vacuum to the cured material.

Some embodiments further include adding 640 particulate matter to thecuring compound. In one embodiment, graphite flakes are added to thepolymerizing material. As non-limiting examples, various embodiments ofthe present invention include the addition of (as referred to atwww.graphitestore.com) Microfyne graphite (approx. 325 mesh); #2 MediumFlake (approx. 200 mesh); and #1 Large Flake (approx. 50 mesh).Generally, these mesh sizes correspond to particle diameters of about40-50 microns, 70-80 microns, and 290-310 microns, respectively. In oneembodiment, the present invention contemplates the addition of fromabout 0.5 percent to about 1 percent (by weight) particulate matter,such as graphite, to the curing material. However, various otherembodiments contemplate the addition from about 0.2 percent to about 5percent by weight.

Process 600 further includes placing 650 the curing mixed material intothe mold. In some embodiments, the method further includes permitting660 the polymerization process to continue at substantially ambientpressure. In such embodiments, there is no attempt to apply a partialvacuum to the curing material during the earliest stages of curingactivity. Instead, various embodiments contemplate the curing of themixed material at substantially ambient pressure for at least about 5minutes. In some embodiments, this period of initial polymerization isallowed to continue for 10 minutes, and in yet other embodiments for 20minutes. During this initial period, polymerization and cross-linking ofthe mixed material begins and continues.

Process 600 further includes applying 670 a subatmospheric pressure tothe material in the mold cavity. In some embodiments, the application ofsubatmospheric pressure encourages the material to foam, withoutsubstantially letting any entrapped gases escape. However, in yet otherembodiments, the present invention contemplates the introduction ofsmall amounts of gas from the mold cavity into the curing material whilethe subatmospheric conditions are maintained on top of the curingmaterial. In such embodiments, this gas reintroduced into the materialthrough the mold cavity replaces any gas that was inadvertently removed,such as by application of excessive vacuum, or application of vacuumbefore significant cross-linking has occurred. Preferably, thesubatmospheric conditions are exposed to the curing material for theremainder of the cure cycle (such as for several hours).

After the material is cured, the vacuum is removed, at which time it ispossible that the final, cured compound reduces in height. The compoundis removed from the mold, and further processed as described below byintroducing fluids into the geometric voids. These steps are depicted asblocks 680 and 690. In block 690 after the material is removed from themold, since the location of geometric features are well known, a fluidis introduced into the geometric features, while allowing air to escapefrom the features. Once the air is removed, the material may beconfigured to automatically close around where the fluid is introduced,or alternatively a repair process followed to repair the locations wherethe fluid is introduced. As discussed above, a fusing process may beneeded in order to provide the geometric features as material portionsare removed from the mold. The fusing process may include melting andcooling, gluing, or other approaches.

It should be appreciated that the above-described blast/shockwavemitigation material can be used in panels to be placed on the bottom,sides, and/or top of military and civilian vehicles in order to makethese vehicles more resistant to blasts from an explosive event such asexplosion of a land mine, or an improvised explosive device.

It should further be appreciated that the above-describedblast/shockwave mitigation material can be used in military helmets toresist shockwave from an arms fire, e.g., a small caliber roundimpacting the helmet. The helmet may be configured to include theabove-described blast/shockwave mitigation material as being sandwichedbetween a metal matrix or composite outer shell and a metal matrix orcomposite inner shell.

It should be appreciated that for the purposes of blast/shockwavemitigation, a multilayer approach can be configured to provideadditional mitigation. A multilayer structure includes a plurality oflayers of impact absorbing material (e.g., a foam material withinclusions of different feature sizes, as described herein), affixed toa blast/shockwave mitigating material (same as the impact absorptionmaterial but with some of the inclusion filled with a fluid other thanair), and affixed to a solid foam material. These various layers act asdiscontinuities for propagation of waves due to impact, blast or shock,thereby causing significant attenuation in the wave. In addition, platesmade from metals, metal matrices, or composites can be providedinterdisposed between these various layers which can provide additionalstructural rigidity and support.

While the inventions have been illustrated and described in detail inthe drawings and foregoing description, the same is to be considered asillustrative and not restrictive in character, it being understood thatonly certain embodiments have been shown and described and that allchanges and modifications that come within the spirit of the inventionare desired to be protected.

What is claimed is:
 1. A composite material for protection of an objectfrom a blast or shock wave, comprising: an impact absorbing materialincluding a plurality of regions, each said region formed as a solidmatrix within which stress-concentrating features are dispersed,including: a plurality of first features dispersed within a firstregion, and having a first average characteristic dimension of betweenabout ten microns and about two hundred microns; a plurality of secondfeatures dispersed within a second region, and having a second averagecharacteristic dimension that is at least about one order of magnitudelarger than said first average characteristic dimension; and a pluralityof third features dispersed within a third region, and having a thirdaverage characteristic dimension that is at least about one order ofmagnitude larger than said second average characteristic dimension;wherein the material proximate to said first, second, and third featuresprogressively buckles upon application of a load, such that materialproximate said third features tends to deform before the deformation ofmaterial proximate to said second and first features, and materialproximate said first features tends to deform after the deformation ofmaterial proximate to said second and third features, and whereinfeatures belonging to any one of said first, second, or third featuresare filled with a fluid other than air.
 2. The composite material ofclaim 1, wherein the filling fluid is water.
 3. The composite materialof claim 1, wherein the filling fluid is oil.
 4. The composite materialof claim 1, wherein the filling fluid is uncured silicone.